Problem: Simplify the following expression: $\sqrt{52}-\sqrt{13}+\sqrt{325}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{52}-\sqrt{13}+\sqrt{325}$ $= \sqrt{4 \cdot 13}-\sqrt{13}+\sqrt{25 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{13}-\sqrt{13}+\sqrt{25} \cdot \sqrt{13}$ $= 2\sqrt{13}-\sqrt{13}+5\sqrt{13}$ Finally, simplify by combining the terms. $= ( 2 - 1 + 5 )\sqrt{13} = 6\sqrt{13}$